Enables DNA-binding transcription repressor activity, RNA polymerase II-specific. Involved in several processes, including intracellular glucose homeostasis; negative regulation of autophagy; and regulation of DNA-templated transcription. Located in cytoplasm and nucleus. Is expressed in several structures, including blastocyst; nervous system; reproductive system; and urinary system. Orthologous to human FOXK2 (forkhead box K2).